Find the sub-interval of
\[
(0,\infty)
\]
in which
\[
f(x)=x^2e^{-x}
\]
is increasing.
Show Hint
Exponential terms like \( e^{-x} \) or \( e^{x} \) can never be negative or zero for any real \( x \). You can divide them out of inequalities safely without changing the inequality sign direction.